<p>In the big data era, image security for real-time processing become more and more important, but they are also difficult in providing security concerns. Many image encryption techniques have been designed using principles of chaos theory on quantum cryptography. Due to their tiny chaotic space, certain low-dimensional chaotic maps can be easily predicted and the encrypted images can be exposed. Motivated by this, the effectiveness of quantum image cryptography using the two distinct chaotic maps is utilized independently to scramble the images. In order to change input image data from the first pixel to the last pixel, forward diffusion is taken into consideration after the quantum key has been produced using the hash256 algorithm. Following that, the input image is scrambled using the Arnold cat map, chaotic bakers map, and logistic map with the osprey optimization algorithm (OOA). OOA is utilized to enhance the performance of the Arnold cat map by optimally selecting the value of p and q with the range from 3 to 10 which ensures robust security, efficient computation, and effective pixel diffusion and confusion. At last, the backward diffusion process and bit-level permutation are taken into account for the scrambled images. In order to evaluate the efficacy of quantum image cryptography based on two chaotic maps, NPCR, UACI, entropy, SSIM, correlation characteristics, and histogram analysis are checked. According to this analysis, the chaotic bakers and pixel permutation maps are not as effective as the Arnold cat map. The obtained values for the Arnold cat map’s UACI, SSIM, and NPCR based on the CASIA2 dataset are improved than the pixel permutation and chaotic bakers map. Thus, the quantum image cryptography based on discrete chaotic maps, such as the Arnold cat map, outperforms the chaotic bakers map and standard pixel permutation technique according to the attained values for the statistical and differential analysis.</p>